Why is my animation choppy when I render it?
This can happen when fast moving objects result in a large difference between consecutive frames.
For reference, here's what my test scene looks like at 24 fps without any motion blur:

To fix this, you have a couple options:
Increase the framerate
Increase the framerate, adding more frames while keeping the same run time.
AFAIK youtube will play high framerate videos at a reduced framerate at lower user-set quality levels, so this may not be an ideal solution for youtube (the results may not be the same for all youtube quality settings).
Here's the same scene at 60fps (click the gif to see a better version):

Add some motion blur
Add some motion blur to smooth the transition between frames
See the manual for details on how to use motion blur in blender internal and in cycles.

Or both
Of course, you can do both at once too ;)
Again, click the gif to see it in a video format..


Unfortunately gifs make terrible examples when showing framerate settings and SE doesn't support embedding of other formats. Click on any of the gifs to see it in a video format.